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Full text of "Engineer field book"

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7 .^ j/\ ^Mj rf 






M - fffi^: 



■^ 



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^^d^iit 



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^^^ 



cr/j^-,: 






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12^X/V 









3J: 



SZZ 












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z^^z 



/s^y^ 









V-'/^^ 
^£^ 



f/o 









JLLi 



y7/V4^ A^^^Y 



f9^ 



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r-?^ 



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S.J a An ^O-. 






':^<r Mtii. 



Jf /^M^ i ^ \ A^ ^ 



/^. \ vA My^jj^ 



1 






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'\,-y 













^^ 



r . 



r 



^z;? ^ ^t^/T e 






/ 

































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^^Yff \ 






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M^ ''- ^^-- 


J^c 




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A^S 


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r ^ ^^ *y* 




9 .' } 


7 t.. 










f f'J^o 


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S^Crt 


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T 1 j L 


A///r% 






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/^/4r7 ^5-A^ ^^^^0<^^i. 



SLOPE REDUCTIONS 

When distances are measured on a slope they may be reduced to 
the equivalent horizontal distance by the following approximate 
rule: subtract from the slope distance the square of the rise divided 
by twice the slope distance. Thus for a slope distance of 250.3 ft. 
and a rise of 15 ft. correction= 152-^2X250.3 = . 45 (by slide rule) 
or horizontal distance^ 250.3 — .45 = 249.85. When vertical angle = 
V. A. is measured horizontal distance = slope distance — slope distance 
(1-Cos V. A.). Thus for slope distance of 248.7 ft. and V. A. of 
4°20" from Table VIII Cos = . 99714 and correctional -.99714 = 
.00286 per foot or total of .286 X 2}^ (near enough) = .57 and horizontal 
distance=248.7-.57 = 248.13 ft. 

See fig. (a). TRIGONOMETRICAL FORMULAS 




Formula for Solving Triangles 





Given 


a, 


C 


a, 


h 


A 


a 


A 


b 


A 


c 




Given 


A 


B, a 


A 


a, b 


a, 


b, C 


a, 


b, c 


A 


B, C, a 


A, 


6, c 


a, 


6, c 



Sought 

A, B, b 

A, B, c 

B, 6, c 
B, a, c 
B, a, b 

Sought 
b 
B 
A-B 



area 
area 
area 



Right triangles. See fig. (a). 
sin A = ~, cos B=j, 6= \/(c+a) (c-a) 
tan A = j, cot B=j, c=^^2 
B=QO°-A, b = a cot A, c=- 

B=90°-^ a = 6tan A, c= 

' c 

B=90° — ^. a = c sin ^, 6 = ccos^ 
Oblique triangles. See fig. (b). 



sin^ 
cos ^ 



sin A 

b sin A 



sin B 

a 

tan H (^-B) = ^°-^^ tan^M+B) 
a-\-b 

' li s=y2 (a + 6-fc), sin K A = J'^^^ 

V 6 c 



cos )i ^ = J^;=^>, tan y2.^ = J('-^)(«-' 

^ — ZVfa-a) (»-6) («-c) « 



6c 



area = 
area 



g^ sin J3sin C 



2 sin A 
y2 b c sin A 
s=y2.(a + 6-hc), area= Vs (s-a)(s-b)(8-c) 



II 



Table I. — Natural Trigonometrical Functions 


Angle 


Sine. 


Tan. 


Cotg. 


Cosin. 




Angle 


Sine. 


Tan. 


Cotg. 


Cosin. 




0/ 









00 


1 


90 


0/ 
8 


.1392 


.1405 


7.115 


.99027 


82 


10 


.0029 


.0029 


343.8 


I 


50 


10 


.1421 


.1435 


6.968 


. 98986 


50 


20 


.0058 


.0058 


171.9 


.99998 


40 


20 


.1449 


.1465 


6.827 


. 98944 


40 


30 1 


.0087 


.0087 


114.6 


.99996 


30 


30 


.1478 


.1495 


6.691 


.98902 


30 


40 


.0116 


.0116 


85.94 


. 99993 


20 


40 


.1507 


.1524 


6.561 


.98858 


20 


50 


.0145 


.0145 


68.75 


.99989 


10 


50 


.1536 


.1554 


6.435 


. 98814 


10 


1 


.0175 


.0175 


57.29 


. 99985 


89 


9 


.1564 


.1584 


6.314 


.98769 


81 


10 


.0204 


.0204 


49.10 


.99979 


50 


10 


.1593 


.1614 


6.197 


. 98723 


50 


20 


.0233 


.0233 


42.96 


. 99973 


40 


20 


.1622 


.1644 


6.084 


. 98676 


40 


30 


.0262 


.0262 


38.19 


.99966 


30 


30 


.1650 


.1673 


5.976 


.98629 


30 


40 


.0291 


.0291 


34.37 


.99958 


20 


40 


.1679 


.1703 


5.871 


.98580 


20 


50 


.0320 


.0320 


31.24 


. 99949 


10 


50 


.1708 


.1733 


5.769 


.98531 


10 


2 


.0349 


.0349 


28.64 


. 99939 


88 


10 


.1736 


.1763 


5.671 


. 98481 


80 


10 


.0378 


.0378 


26.43 


.99929 


50 


10 


.1765 


.1793 


5.576 


.98430 


50 


20 


.0407 


.0407 


24.54 


. 99917 


40 


20 


.1794 


.1823 


5.485 


. 98378 


40 


30 


.0436 


.0437 


22.90 


.99905 


30 


30 


.1822 


.1853 


5.396 


. 98325 


30 


40 


.0465 


.0466 


21.47 


. 99892 


20 


40 


.1851 


.1883 


5.309 


.98272 


20 


50 


.0494 


.0495 


20.21 


. 99878 


10 


50 


.1880 


.1914 


5.226 


.98218 


10 


3 


.0523 


.0524 


19.08 


. 99863 


87 


11 


.1908 


.1944 


5.145 


. 98163 


79 


10 


.0552 


.0553 


18.07 


. 99847 


50 


10 


.1937 


.1974 


5.066 


.98107 


50 


20 


.0581 


.0582 


17.17 


. 99831 


40 


20 


.1965 


.2004 


4.989 


.98050 


40 


30 


.0610 


.0612 


16.35 


.99813 


30 


30 


.1994 


.2035 


4.915 


.97992 


30 


40 


.0640 


.0641 


15.60 


. 99795 


20 


40 


. 2022 


.2065 


4.843 


.97934 


20 


50 


.0669 


.0670 


14.92 


. 99776 


10 


50 


.2051 


.2095 


4.773 


. 97875 


10 


4 


.0698 


.0699 


14.30 


.99756 


86 


12 


.2079 


.2126 


4.705 


. 97815 


78 


10 


.0727 


.0729 


13.73 


.99736 


50 


10 


.2108 


.2156 


4.638 


.97754 


50 


20 


.0756 


.0758 


13.20 


. 99714 


40 


20 


.2136 


.2186 


4.574 


. 97692 


40 


30 


.0785 


.0787 


12.71 


.99692 


30 


30 


.2164 


.2217 


4.511 


. 97630 


30 


40 


.0814 


.0816 


12.25 


.99668 


20 


40 


.2193 


.2247 


4.449 


. 97566 


20 


50 


.0843 


.0846 


11.83 


.99644 


10 


50 


.2221 


.2278 


4.390 


. 97502 


10 


5 


.0872 


.0875 


11.43 


.99619 


85 


13 


.2250 


.2309 


4.331 


. 97437 


77 


10 


.0901 


.0904 


11.06 


.99594 


50 


10 


.2278 


.2339 


4.275 


.97371 


60 


20 


.0929 


.0934 


10.71 


.99567 


40 


20 


.2306 


.2370 


4.219 


.97304 


40 


30 


.09.58 


.0963 


10. 39 


.99540 


30 


30 


.2334 


.2401 


4.165 


.97237 


30 


40 


0987 


.0992 


10.08 


.99511 


20 


40 


.2363 


.2432 


4.113 


.97169 


20 


50 


.1016 


.1022 


9.788 


.99482 


10 


50 


.2391 


.2462 


4.061 


.97100 


10 


6 


. 1045 


. 1051 


9.514 


.99452 


84 


14 


.2419 


.2493 


4.011 


. 97030 


7S 


10 


. 1074 


.1080 


9.255 


.99421 


50 


10 


.2447 


.2524 


3.962 


.96959 


50 


20 


. 1103 


. 1110 


9.010 


.99390 


40 


20 


.2476 


.2555 


3.914 


.96887 


40 


30 


. 1132 


. 1139 


8.777 


.99357 


30 


30 


.2504 


.2586 


3.867 


.96815 


30 


40 


1161 


. 1169 


8. 556 


.99324 


20 


40 


. 2532 


.2617 


3.821 


.96742 


20 


50 


.1190 


.1198 


8.345 


.99290 


10 


50 


.2560 


.2648 


3.776 


.96667 


10 


7 


. 1219 


. 1228 


8. 144 


. 99255 


83 


16 


.2588 


.2679 


3. 732 


. 96593 


75 


10 


. 1248 


. 1257 


7. 95.3 


. 99219 


50 


10 


.2616 


.2711 


3.689 


. %517 


50 


20 


. 1276 


. 1287 


7. 770 


.99182 


40 


20 


.2644 


.2742 


3.647 


.96440 


40 


M 


. 1305 


. 1317 


7. 596 


.99144 


30 


30 


.2672 


. 2773 


3.606 


.96363 


30 


40 


1334 


. 1346 


7.429 


.99106 


20 


40 


.2700 


.2805 


3.566 


.96285 


20 


60 


.1363 


.1376 


7.269 


.99067 


10 
81 


50 


.2728 


.2836 


3.626 


.96206 


10 
74 




('osin 


Cotg. 


Tan. 


Sine. 


Angle 




rosin. 


Cotg. 


Tan. 


Sine. 


Anglo 



























Ill 





Table I. — Natura 


L Trigonom 


ETRicAL Functions 




Angle 


Sine. 


Tan. 


Cotg. 


Cosin. 




Angle 


Sine. 


Tan. 


Cotg. 


Cosin. 




16 


.2756 


.2867 


3.487 


.96126 


74 


0/ 

24 


.4067 


.4452 


2.246 


. 91355 


66 


10 


.2784 


.2899 


3.450 


.96046 


50 


10 


.4094 


.4487 


2.229 


. 91236 


60 


20 


.2812 


.2931 


3.412 


.95964 


40 


20 


.4120 


.4522 


2.211 


.91116 


40 


30 


.2840 


.2962 


3.376 


. 95882 


30 


30 


.4147 


. 4557 


2.194 


.90996 


30 


40 


.2868 


.2994 


3.340 


. 95799 


20 


40 


.4173 


. 4592 


2.177 


. 90875 


20 


50 


.2896 


.3026 


3. 305 


. 95715 


10 


50 


.4200 


.4628 


2.161 


. 90753 


10 


17 


.2924 


.3057 


3.271 


. 95615 


73 


25 


.4226 


.4663 


2.145 


. 90631 


65 


10 


.2952 


.3089 


3.237 


.95545 


50 


10 


.4253 


. 4699 


2.128 


. 90507 


50 


20 


.2979 


.3121 


3.204 


.95459 


40 


20 


.4279 


.4734 


2.112 


. 90383 


40 


30 


.3007 


.3153 


3.172 


. 95372 


30 


30 


.4305 


.4770 


2.097 


. 90259 


30 


40 


.3035 


.3185 


3.140 


.95284 


20 


40 


.4331 


.4806 


2.081 


. 90133 


20 


50 


.3062 


.3217 


3.108 


. 95195 


10 


50 


.4358 


.4841 


2.066 


.90007 


10 


18 


.3090 


.3249 


3.078 


. 95106 


72 


26 


.4384 


.4877 


2.050 


. 89879 


64 


10 


.3118 


.3281 


3.048 


. 95015 


50 


10 


.4410 


.4913 


2. 035 


. 89752 


50 


20 


.3145 


.3314 


3.018 


. 94924 


40 


20 


.4436 


.4950 


2.020 


. 89623 


40 


30 


.3173 


.3346 


2.989 


. 94832 


30 


30 


.4462 


.4986 


2.006 


.89493 


30 


40 


.3201 


.3378 


2.960 


. 94740 


20 


40 


.4488 


.5022 


1.991 


. 89363 


20 


50 


.3228 


.3411 


2.932 


. 94646 


10 


50 


.4514 


.5059 


1.977 


. 89232 


10 


19 


.3256 


.3443 


2.904 


. 94552 


71 


27 


. 4540 


.5095 


1.963 


. 89101 


63 


10 


.3283 


.3476 


2.877 


. 94457 


50 


10 


.4566 


.5132 


1.949 


. 88968 


50 


20 


.3311 


.3508 


2.850 


. 94361 


40 


20 


.4592 


.5169 


1.935 


.88835 


40 


30 


.3338 


.3541 


2.824 


. 94264 


30 


30 


.4617 


.5206 


1.921 


. 88701 


30 


40 


.3365 


.3574 


2.798 


.94167 


20 


40 


.4643 


.5243 


1.907 


. 88566 


20 


50 


.3393 


.3607 


2.773 


.94068 


10 


50 


.4669 


.5280 


1.894 


.88431 


10 


20 


.3420 


.3640 


2.747 


. 93969 


70 


28 


.4695 


.5317 


1.881 


.88295 


62 


10 


.3448 


.3673 


2.723 


. 93869 


50 


10 


.4720 


.5354 


1.868 


. 88158 


50 


20 


.3475 


.3706 


2.699 


. 93769 


40 


20 


.4746 


.5392 


1. 855 


.88020 


40 


30 


. 3502 


.3739 


2.675 


. 93667 


30 


30 


.4772 


.5430 


1.842 


. 87882 


30 


40 


.3529 


.3772 


2.651 


. 93565 


20 


40 


.4797 


.5467 


1.829 


. 87743 


20 


50 


.3557 


.3805 


2.628 


. 93462 


10 


50 


.4823 


.5505 


1.816 


. 87603 


10 


21 


.3584 


.3839 


2.605 


.93358 


69 


29 


.4848 


.5543 


1.804 


. 87462 


61 


10 


.3611 


.3872 


2.583 


. 93253 


50 


10 


.4874 


.5581 


1.792 


. 87321 


50 


20 


.3638 


.3906 


2.560 


. 93148 


40 


20 


.4899 


.5619 


1.780 


. 87178 


40 


30 


.3665 


.3939 


2.539 


. 93042 


30 


30 


.4924 


.5658 


1.767 


. 87036 


30 


40 


.3692 


.3973 


2.517 


. 92935 


20 


40 


. 4950 


.5696 


1.756 


.86892 


20 


50 


.3719 


.4006 


2.496 


. 92827 


10 


50 


.4975 


.5735 


1.744 


. 86748 


10 


n 


.3746 


.4040 


2.475 


. 92718 


68 


30 


.5000 


.5774 


1.732 


. 86603 


60 


10 


.3773 


.4074 


2.455 


.92609 


50 


10 


.5025 


.5812 


1.720 


.86457 


50 


20 


.3800 


.4108 


2.434 


. 92499 


40 


20 


.5050 


.5851 


1.709 


. 86310 


40 


30 


.3827 


.4142 


2.414 


.92388 


30 


30 


.5075 


.5890 


1.698 


. 86163 


30 


40 


.3854 


.4176 


2.394 


. 92276 


20 


40 


.5100 


.5930 


1.686 


. 86015 


20 


50 


.3881 


.4210 


2.375 


. 92164 


10 


50 


. 5125 


.5969 


1.675 


.85866 


10 


23 


.3907 


.4245 


2.356 


.92050 


67 


31 


.5150 


.6009 


1.664 


. 85717 


59 


10 


.3934 


.4279 


2. 337 


. 91936 


50 


10 


.5175 


.6048 


1.653 


. 85567 


50 


20 


.3961 


.4314 


2.318 


.91822 


40 


20 


.5200 


.6088 


1.643 


. 85416 


40 


30 


.3987 


.4348 


2.300 


. 91706 


30 


30 


.5225 


.6128 


1.632 


.85264 


30 


40 


.4014 


.4383 


2.2o2 


.91590 


20 


40 


.5250 


.6168 


1.621 


.85112 


20 


50 


.4041 


.4417 


2.264 


. 91472 


10 
66 


50 


.5275 


.6208 


1.611 


. 84959 


10 

58 




Cosin. 


Cotg. 


Tan. 


Sine. 


Angle 




Cosin. 


Cotg. 


Tan. 


Sine. 


Angle 





IV 





Table I 


. — Natural Trigonometrical Functions 




Angle 


Sine. 


Tan. 


Cotg. 


Cosin. 




Angle 


Sine. 


Tan. 


Cotg. 


Cosin. 




0/ 
32 


.5299 


.6249 


1.600 


.84805 


58 


0/ 
30 


.6225 


.7954 


1.257 


. 78261 


30 


10 


.5324 


.6289 


1.590 


. 84650 


50 


40 


.6248 


.8002 


1.250 


. 78079 


20 


20 


.5348 


.6330 


1.580 


. 84495 


40 


50 


.6271 


.8050 


1.242 


. 77897 


10 


30 


.5373 


.6371 


1.570 


. 84339 


30 














40 


.5398 


.6412 


1.560 


. 84182 


20 


39 


.6293 


.8098 


1.235 


. 77715 


51 


50 


.5422 


.6453 


1.550 


.84025 


10 


10 


.6316 


.8146 


1.228 


. 77531 


50 














20 


.6338 


.8195 


1.220 


. 77347 


40 


33 


.5446 


.6494 


1.540 


. 83867 


67 


30 


.6361 


.8243 


1.213 


. 77162 


30 


10 


.5471 


.6536 


1.530 


.83708 


50 


40 


.6383 


.8292 


1.206 


. 76977 


20 


20 


.5495 


.6577 


1.520 


.83549 


40 


50 


.6406 


.8342 


1.199 


.76791 


10 


30 


.5519 


.6619 


L511 


.83389 


30 














40 


.5544 


.6661 


1.501 


.83228 


20 


40 


.6428 


.8391 


1.192 


.76604 


50 


50 


.5568 


.6703 


L492 


.83066 


10 


10 


.6450 


.8441 


1.185 


.76417 


50 














20 


.6472 


.8491 


1.178 


.76229 


40 


34 


.5592 


.6745 


1.483 


.82904 


56 


30 


.6494 


.8541 


1.171 


.76041 


30 


10 


.5616 


.6787 


L473 


. 82741 


50 


40 


.6517 


.8591 


1.164 


.75851 


20 


20 


.5640 


.6830 


1.464 


. 82577 


40 


50 


.6539 


.8642 


L157 


. 75661 


10 


30 


.5664 


.6873 


L455 


.82413 


30 














40 


.5688 


.6916 


1.446 


.82248 


20 


41 


.6561 


.8693 


1.150 


.75471 


49 


50 


.5712 


.6959 


1.437 


.82082 


10 


10 


.6583 


.8744 


1.144 


.75280 


50 














20 


.6604 


.8796 


1.137 


.75088 


40 


35 


.5736 


.7002 


1.428 


.81915 


55 


30 


.6626 


.8847 


1.130 


.74896 


30 


10 


.5760 


.7046 


1.419 


. 81748 


50 


40 


.6648 


.8899 


1.124 


. 74703 


20 


20 


.5783 


.7089 


1.411 


.81580 


40 


50 


.6670 


.8952 


1.117 


.74509 


10 


30 


.5807 


.7133 


1.402 


.81412 


30 














4b 


.5831 


.7177 


1. 393 


. 81242 


20 


42 


.6691 


.9004 


1.111 


. 74314 


48 


50 


.5854 


.7221 


1.385 


.81072 


10 


10 


.6713 


.9057 


1.104 


. 74120 


50 














20 


.6734 


.9110 


1.098 


. 73924 


40 


36 


.5878 


.7265 


1.376 


.80902 


54 


30 


.6756 


.9163 


1.091 


. 73728 


30 


10 


.5901 


.7310 


1.368 


.80730 


50 


40 


.6777 


.9217 


1.085 


.73531 


20 


20 


.5925 


.7355 


1.360 


.80558 


40 


50 


.6799 


.9271 


1.079 


. 73333 


10 


30 


.5948 


.7400 


1.351 


. 80386 


30 














40 


.5972 


.7445 


1.343 


.80212 


20 


43 


.6820 


. y: 25 


1.072 


. 73135 


47 


50 


.5995 


.7490 


1.335 


.80038 


10 


10 


.6841 


.9380 


1.066 


. 72937 


50 














20 


.6862 


. 9435 


1.060 


. 72737 


40 


87 


.6018 


.7536 


1.327 


.79864 


53 


30 


.6884 


.9490 


1.054 


. 72537 


30 


10 


.6041 


.7581 


1.319 


.79688 


50 


40 


.6905 


.9545 


1.048 


. 72337 


20 


20 


. 6065 


.7627 


1.311 


. 79512 


40 


60 


.6926 


.9601 


1.042 


. 72136 


10 


30 


.6088 


.7673 


1. 303 


. 79335 


30 














40 


.6111 


.7720 


1.295 


.79158 


20 


44 


.6947 


. 9657 


1.036 


. 71934 


46 


60 


.6134 


.7766 


L288 


.78980 


10 


10 


.6967 


.9713 


1.030 


.71732 


50 














20 


.6988 


.9770 


1.024 


.71529 


40 


38 


.6157 


.7813 


1.280 


.78801 


52 


30 


.7009 


.9827 


1.018 


.71325 


30 


10 


.6180 


.7860 


1.272 


.78622 


60 


40 


. 7030 


.9884 


1.012 


.71121 


20 


20 


.6202 


.7907 


1.265 


.78442 


40 


60 


.7050 
.7071 


.9942 
1. 


1.006 
1. 


.70916 
.70711 


10 
45 




Coftln. 


Cotg. 


Tan. 


Sine. 


Angle 




Casin. 


Cotg. 


Tan. 


Sine. 


Anglo 









Table II.— 


-Calculation of Earthwork 






5 


HEIGHT 


1 
.02 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


1 


.04 


.06 


.07 


.09 


.11 


.13 


.15 


.17 


.18 


.20 


.22 


.24 


.26 


.28 


3 


.04 


,07 


.11 


.15 


.18 


.22 


.26 


.30 


.33 


.37 


.41 


.44 


.48 


.52 


.56 


3 


.06 


.11 


.17 


.22 


.28 


.33 


.39 


.44 


.50 


.56 


.61 


-67 


.72 


.78 


.83 


4 


.07 


.15 


.22 


.30 


.37 


.44 


.52 


.59 


.67 


.74 


.81 


-89 


.96 


L04 


Lll 


5 


.09 


.19 


.28 


.37 


.46 


.56 


.65 


.74 


.83 


.93 


L02 


Lll 


L20 


L30 


L39 


6 


.11 


.22 


.33 


.44 


.56 


.67 


.78 


.89 loo' Lll 


L22 


L33 


L44 


L55 


L67 


7 


.13 


.26 


.39 


.52 


.65 


.78 


.91 


L04| L16' L30 


L42 


1.55 


L68 


L81 


L94 


8 


.15 


.30 


.44 


.59 


.74 


.89 


L04 


1.19! 1.33 L48 


1.63 


L78 


1.92 


2.08 


2.22 


1 


-17 


.33 


.50 


.67 


.83 


1.00 


L17 


L33 1.50 L67 


L83 


2.00 


2.17 


2.33 


2.50 


if 


.18 


.37 


.56 


.74 


.93 


Lll 


L30 


L48 1.671 L85 


2.04 


2.22 


2.41 


2.59 


2.78 


11 


.20 


.41 


.61 


.82 


1.02 


1.22 


1.43 


L63 1.83' 2.04 


2.24 


2.44 


2.65 


2.85 


3.06 


1? 


.22 


.44 


.67 


.89 


1.11 


1.33 1.56 


1.78 2.00 2.22 


2.44 


2.67 


2.89 


3.11 


3.33 


IS 


.24 


.48 


.72 


.96 


1.20 


1.44! 1.68 


1.92 2.16 2.41 


2.65 


2.89 


3.13 


3.37 


3.61 


14 


.26 


.52 


.78 


1.04 


1.30 


L55 1.81 


2.08 2.33 2.59 


2.85 


3.11 


3.37 


3.63 


3.89 


15 


.28 


-56 


.83 


1.11 


1.39 


L67 L94 


2.22 2.50, 2.78 


3.06 


3.33 


3.61 


3.89 


4.17 


16 


.30 


.59 


.89 


1.18 


1.48 


1.78' 2.07 


2.37 2.67! 2.96 


3.26 


3.56 


3.85 


4.15 


4.44 


17 


.31 


.63 


.94 


1.26 


1.57 


L89' 2.20 


2.52 2.83 3.15 


3.46 


3.78 


4.09 


4.41 


4.72 


18 


.33 


.67 


1.00 


1-.33 


1.67 


2.00 2.33 


2.67 3.00 3.33 


3.67 


4.00 


4.33 


4.67 


5.00 


If 


.35 


.70 


1.06 


1.41 


1.76 


2.11, 2.46 


2.82, 3.17 


3.52 


3.87 


4.22 


4.57 


4.92 


5.28 


20 


.37 


.74 


1.11 


1.48 


1.85 


2.22 


2.59 


2.96 3.33 


3.70 


4.07 


4.44 


4.81 


5.18 


5.56 


21 


.39 


.78 


1.17 


1.55 


1.94 


2.33 


2.72 


3.11 3.50 


3.89 


4.28 


4.67 


5.06 


5.44 


5.83 


W 


.41 


.81 


1.22 


1.63 


2.04 


2.44 


2.85 


3.26! 3.67 


4.07 


4.48 


4.89 


5.30 


5.70 


6.11 


23 


.43 


.85 


1.28 


1.70 


2.13 


2.56' 2.98 


3.41 3.831 4.26 


4.68 


5.11 


5.54 


5.96 


6.39 


24 


.44 


.89 


1.33 


1.78 


2.22 


2.67 


3.11 


3.56 4.00, 4.44 


4.89 


5.33 


5.78 


6.22 


6.67 


25 


.46 


.92 


1.39 


1.85 


2.31 


2.78 


3.24 


3.70 


4.17 


4.63 


5.09 


5.56 


6.02 


6.48 


6.94 


26 


.48 


.96 


1.44 


1.92 


2.41 


2.89 


3.37 


3.85 


4.33 


4.82 


5.30 


5.78 


6.26 


6.74 


7.24 


27 


.50 


1.00 


1.50 


2.00 


2.50 


3.00 


3.50 


4.00 


4.50 


5.00 


5.50 


6.00 


6.50 


7.00 


7.50 


28 


.52 


1.04 


1.55 


2.07 


2.59 


3.11 


3.63 


4.15 


4.67 


5.18 


5.70 


6.22 


6.74 


7.26 


7.78 


2f 


.54 


1.07 


1.61 


2.15 


2.68 


3.22 


3.76 


4.30 


4.83 


5.37 


5.91 


6.44 


6.98 


7.52 


8.06 


3f 


.56 


1.11 


1.67 


2.22 


2.78 


3.33 


3.89 


4.44 


5.00 


5.55 


6.11 


6.67 


7.22 


7.78 


8.33 


SI 


.57 


1.15 


1.72 


2.30 


2.87 


3.44 


4.02 


4.59 


5.17 


5.74 


6.32 


6.89 


7.46 


8.04 


8.61 


S2 


.59 


1.18 


1.78 


2.37 


2.96 


3.56 


4.15 


4.74 


5.33! 5.92 


6.52 


7.11 


7.70 


8.30 


8.89 


ss 


.61 


1.22 


1.83 


2.44 


3.05 


3.67 


4.28 


4.89 


5.50 6.11 


6.72 


7.33 


7.94 


8.55 


9.17 


S4 


.63 


1.26 


1.89 


2.52 


3.15 


3.78 


4.40 


5.04 


5.67 6.29 


6.93 


7.56 


8.18 


8.81 


9.44 


S5 


.65 


1.30 


1.94 


2.59 


3.24 


3.89 


4.53 


5.18 


5.83 6.48 


7.13 


7.78 


8.42 


9.08 


9.72 


S6 


.67 


1.33 


2.00 


2.67 


3.33 


4.00 


4.66 


5.33 


6.00 6.67 


7.83 


8.00 


8.67 


9.33 


10.00 


S7 


.68 


1.37 


2.06 


2.74 


3.42 


4.111 4.79 


5.48 


6.17 6.85 


7.54 


8.22 


8.91 


9.59 


10.28 


S8 


.70 


1.41 


2.11 


2.82 


3.52 


4.22 4.92 


5.63 


6.33 7.03 


7.74 


8.44 


9.15 


9.85 


10.56 


Sf 


.72 


1.44 


2.17 


2.89 


3.61 


4.33 5.05 


5.78 


6.50 7.22 


7.95 


8.67 


9.39 


10.11 


10.83 


4f 


.74 


1.48 


2.22 


2.96 


3.70 


4.44 5.18 


5.92 


6.67 7.41 


8.15 


8.89 


9.63 


10.37 


ILll 


Table 


gives 


cu. y( 


Is. in 


1 ft. ( 


Df a triangle 


of given width 


and h 


eight. 


Cor 


rections for 


tenths of 


widtl 


3 are ( 


)ne te 


nth tt 


le values foi 


md under each h 


eight 


consic 


lering 


the widths 


from 1 tc 


9as 


tenths 


> and 


simila 


irly the con 


ections for tenth 


3 of he 


iight 


ire on 


e tenth the 


figures 0] 


aposit 


e wid 


th con 


sideri 


ng the heig 


Its from 1 to 9 as 


tenthj 


,. Th 


lus if 


[vidth = 16.2 


and heig 


ht=5. 


3, cu. 


yds.= 


= 1.48- 


h.028-|-.089= 


= 1.597 cu. yds. or 


prac 


icall> 


160 c 


u. yds. per 


100 ft. I 


f wid 


th exc 


«eds4 


ft., 


use one hal 


f and multiply re 


suit h 


y2, i 


both 


width and 


height ai 


e larg 


e use 


3ne hi 


ilf of e 


ach and mi 


iltiply result by 4 


. Ae 


y cro5 


>s-sect 


ion may be 


divided 


into t 


riangl 


Bs by 


thefc 


)llowing rul 


e. To the triang 


leof 


the su 


m of 


the outside 


cuts (or 
the dista 


fills) = 
nee 01 


= heigb 
It toe 


t, an 
ach b 


i h t 
reak i 


he roadbed 
n turn ( = w 


= width, add the 
idth's) by the dif 


trian 
Teren( 


gles f 
« bet 


ormec 
i^een 


by taking 
he cuts (or 


fills) on 


jach s 


ide of 


it( = 


beight 


's) always . 


>ubtracting the 


iter fr 


om tt 


le inn 


er. 



U. S. GOVERNMENT PRINTING OFFICE : 1952— 0-223453 



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> 



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